Volume of Cube changing with respect to time.

In summary, volume is the amount of space occupied by a three-dimensional object. The volume of a cube is calculated by multiplying its length, width, and height. The volume of a cube can change over time due to changes in its dimensions, temperature or pressure, chemical reactions, and physical processes. To measure the change in volume of a cube over time, various methods such as displacement, water displacement, or using instruments like a graduated cylinder or a balance can be used to track the difference in volume at different points in time.
  • #1
A_Munk3y
72
0

Homework Statement


The volume V of a cube with sides of length x in. is changing with respect to time. At a certain instant of time, the sides of the cube are 5 in. long and increasing at the rate of 0.1 in./sec. How fast is the volume of the cube changing at that instant of time?




The Attempt at a Solution


dv/dt = dx/dt*3x2
dx/dt=0.1 x=5
dv/dt=0.1(3*52)=7.5 cu in/sec

am i correct in my answer?
 
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  • #2
Looks right.
 
  • #3
thanks! :)
 

Related to Volume of Cube changing with respect to time.

What is the definition of volume?

Volume is the amount of space occupied by a three-dimensional object.

How is the volume of a cube calculated?

The volume of a cube is calculated by multiplying the length, width, and height of the cube. The formula for volume is V = lwh, where V is volume, l is length, w is width, and h is height.

Can the volume of a cube change over time?

Yes, the volume of a cube can change over time if any of its dimensions (length, width, or height) change. For example, if the cube is melting or evaporating, its volume will decrease over time.

What factors can cause the volume of a cube to change?

The volume of a cube can change due to changes in its dimensions, changes in temperature or pressure, chemical reactions, and physical processes such as melting, dissolving, or evaporating.

How can we measure the change in volume of a cube over time?

The change in volume of a cube over time can be measured using various methods such as displacement, water displacement, or by using instruments like a graduated cylinder or a balance. These methods allow us to calculate the difference in volume at different points in time and track the change over time.

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